# How do you find the derivative of y =sqrt(x-1)?

Sep 24, 2014

In this problem we have to use the Power Rule and the Chain Rule.

We begin by converting the radical(square root) to it exponential form.

$y = \sqrt{x - 1} = {\left(x - 1\right)}^{\frac{1}{2}}$

Apply the Chain Rule

$y ' = \frac{1}{2} {\left(x - 1\right)}^{\frac{1}{2} - 1} \cdot \left(1\right)$

$y ' = \frac{1}{2} {\left(x - 1\right)}^{\frac{1}{2} - \frac{2}{2}}$

$y ' = \frac{1}{2} {\left(x - 1\right)}^{- \frac{1}{2}}$

Convert negative exponents to positive exponents

$y ' = \frac{1}{2 {\left(x - 1\right)}^{\frac{1}{2}}}$

Convert positive exponent to radical form

$y ' = \frac{1}{2 \sqrt{x - 1}}$